Method and System for Pore-Scale Modeling of a Multi-Phase Hydrocarbon Extraction Process

Abstract

A computer system models a hydrocarbon extraction process using a dynamic pore network model that is generated to represent a subterranean reservoir containing hydrocarbons as pores connected by throats. Solvent is injected into the subterranean reservoir to mobilize the hydrocarbons for extraction thereof. An iterative process may be repeated over time to determine hydrocarbon extraction based on changes in the molar balance of the components over time. A first set of characteristics for each pore is defined from which a second set of characteristics can be derived for two-phase pores. The molar balance of the components is determined based on the first and second sets of characteristics. The first set of characteristics is updated based on the molar balance of the components and the process can be repeated for subsequent times. Parameters for injection of the solvent may be adjusted and the iterative process repeated over time to identify preferred parameters.

1 . A method of operating a computer system for determining hydrocarbon extraction from a subterranean reservoir, the method comprising:
 a) generating a pore network model of the subterranean reservoir representing a structure of the subterranean reservoir and conditions in the subterranean reservoir, the structure of the subterranean reservoir being represented by the pore network model as a plurality of pores connected to each other by a plurality of throats, the plurality of pores and the plurality of throats containing components including hydrocarbons;   b) establishing operational parameters for injection of a solvent into the subterranean reservoir represented by the pore network model, wherein the solvent when injected becomes one of the components in at least one from the plurality of pores and the plurality of throats;   c) based on the operational parameters for injection of the solvent, performing:
 i. defining, for each of the plurality of pores, a first set of characteristics based on a molar density of each component in a pore; 
 ii. deriving, for each of the plurality of pores based on phase conditions in the pore, a second set of characteristics for the pore from the first set of characteristics for the pore; 
 iii. determining, for each of the plurality of throats, phase conditions in a throat from the plurality of throats based on the phase conditions in ones of the plurality of pores that are connected to the throat; 
 iv. determining a molar balance of the components within the plurality of pores and the plurality of throats in the pore network model based on the first set of characteristics and the second set of characteristics for each of the plurality of pores and the phase conditions for each of the plurality of throats; 
 v. determining an updated first set of characteristics for each of the plurality of pores based on the molar balance of the components within the pore network model; 
 vi. repeating (ii) to (v) over a predetermined time at consecutive times to determine hydrocarbon extraction from the subterranean reservoir over time given the operational parameters for injection of the solvent based on changes in the molar balance of the components over time representing mass transfer of the components within the pore network model; and 
   d) adjusting the operational parameters for injection of the solvent and repeating (c) with the adjusted operational parameters to identify operational parameters for injection of the solvent that provide a predetermined hydrocarbon extraction.   
     
     
         2 . The method of  claim 1 , wherein generating the pore network model comprises:
 measuring, with at least one capture device, properties of subterranean reservoir representing the structure of the subterranean reservoir and the conditions in the subterranean reservoir;   classifying the properties of the subterranean reservoir representing the structure as representing pore, matrix or throat;   generating the pore network model using the classified properties of pore for the plurality of pores and the classified properties of throat for the plurality of throats; and   establishing the properties representing the conditions in the subterranean reservoir as initial conditions for the pore network model, the initial conditions including liquid saturation in each of the plurality of pores.   
     
     
         3 . The method of  claim 1 , wherein defining, for each of the plurality of pores, the first set of characteristics comprises:
 establishing a constant parameter to represent conditions used in thermodynamic flash calculations;   when the constant parameter is constant volume:
 determining the molar density of each component in the pore network model for each of the plurality of pores as the first set of characteristics; 
   when the constant parameter is constant pressure:
 determining the molar density of each component in the pore network model and one of a gas pressure and a liquid pressure for each of the plurality of pores for the first set of characteristics; 
   and wherein deriving the second set of characteristics comprises:
 determining the phase conditions in each of the plurality of pores by determining whether the components in each of the plurality of pores is in one phase or two phases where one phase is one of a liquid phase and a gas phase and two phases includes both the liquid phase and the gas phase; 
 when the constant parameter is constant volume:
 deriving, from the first set of characteristics, molar density of each component in the liquid phase, molar density of each component in the gas phase and saturation of the liquid phase for each of the plurality of pores that are in two phases as the second set of characteristics; 
 
 when the constant parameter is constant pressure:
 deriving, from the first set of characteristics, a mole fraction of each component in the liquid phase, a mole fraction of each component in the gas phase, saturation of the liquid phase, and saturation of the gas phase for each of the plurality of pores that are in two phases as the second set of characteristics. 
 
   
     
     
         4 . The method of  claim 3 , wherein defining, for each of the plurality of pores, the first set of characteristics when the constant parameter is constant pressure further comprises:
 determining the mole fraction of each component based on the molar density of each component for the first set of characteristics such that the first set of characteristics is the one of the gas pressure and the liquid pressure and the mole fraction of each component.   
     
     
         5 . The method of  claim 3 , wherein determining, for each of the plurality of throats, the phase conditions in the throat comprises:
 determining phase occupancy for each of the plurality of throats by determining whether the components in each of the plurality of throats is in one phase or two phases where one phase is one of a liquid phase and a gas phase and two phases includes both the liquid phase and the gas phase; and   determining phase conductivity of the liquid phase and the gas phase in each of the plurality of throats.   
     
     
         6 . The method of  claim 5 , wherein determining the molar balance of the components comprises:
 determining a representation for the molar balance for each component in the subterranean reservoir based on a geometry of the plurality of pores, a geometry of the plurality of throats, the first set of characteristics for each of the plurality of pores, the second set of characteristics, molar density of each component in the subterranean reservoir, the phase conductivity in each of the plurality of throats, and pressure of each phase in each of the plurality of pores;   employing a numerical analysis method to determine the molar balance for each component for each of the plurality of pores based on the representation of the molar balance for each component and the first set of characteristics for each of the plurality of pores;   determining a change in the first set of characteristics for each of the plurality of pores based on the molar balance from the numerical analysis method;
 wherein based on the operational parameters for injection of the solvent, performing further comprises:
 prior to repeating (ii) to (v) over the predetermined time at consecutive times, iteratively repeating (ii) to (v) for a current time of the consecutive times until the change in the first set of characteristics is less than a predetermined change with respect to a change in the first set of characteristics from a previous iteration at the current time; and 
 
 wherein determining the updated first set of characteristics for each of the plurality of pores comprises:
 updating the first set of characteristics for each of the plurality of pores based on the change in the first set of characteristics determined based on the molar balance from the numerical analysis method. 
 
   
     
     
         7 . The method of  claim 6 , wherein employing the numerical analysis method to determine the molar balance for each component comprises:
 determining a Jacobian matrix representing a rate of change of the representation of the molar balance with respect to a rate of change of the first set of characteristics; and   employing a fully implicit numerical analysis method to determine the molar balance for each component for each of the plurality of pores using the Jacobian matrix.   
     
     
         8 . The method of  claim 1 , wherein determining the updated first set of characteristics for each of the plurality of pores comprises:
 updating the first set of characteristics for each of the plurality of pores based on a change of the molar balance of the components for a corresponding one of the plurality of pores.   
     
     
         9 . The method of  claim 1 , wherein repeating (ii) to (v) over the predetermined time comprises:
 before repeating (ii) to (v), adjusting a time step between the consecutive times if a change in a predetermined characteristic between consecutive times is greater than predetermined amount; and   repeating (ii) to (v) at a new time which is the time step from a current time until the new time is the predetermined time.   
     
     
         10 . The method of  claim 1 , wherein repeating (ii) to (v) over the predetermined time comprises:
 determining the hydrocarbon extraction from the subterranean reservoir based on a difference in the molar balance in the pore network model at a previous consecutive time to the molar balance in the pore network model at a current time.   
     
     
         11 . A computer system for determining hydrocarbon extraction from a subterranean reservoir, the computer system comprising:
 an interface for receiving information about properties of the subterranean reservoir;   a processor configured to:
 a) generate a pore network model of the subterranean reservoir based on the received information about the properties of the subterranean reservoir, the pore network model representing a structure of the subterranean reservoir and conditions in the subterranean reservoir, the structure of the subterranean reservoir being represented by the pore network model as a plurality of pores connected to each other by a plurality of throats, the plurality of pores and the plurality of throats containing components including hydrocarbons; 
 b) establish operational parameters for injection of a solvent into the subterranean reservoir represented by the pore network model, wherein the solvent when injected becomes one of the components in at least one from the plurality of pores and the plurality of throats; 
 c) based on the operational parameters for injection of the solvent, perform:
 i. define, for each of the plurality of pores, a first set of characteristics based on a molar density of each component in a pore; 
 ii. derive, for each of the plurality of pores based on phase conditions in the pore, a second set of characteristics for the pore from the first set of characteristics for the pore; 
 iii. determine, for each of the plurality of throats, phase conditions in a throat from the plurality of throats based on the phase conditions in ones of the plurality of pores that are connected to the throat; 
 iv. determine a molar balance of the components within the plurality of pores and the plurality of throats in the pore network model based on the first set of characteristics and the second set of characteristics for each of the plurality of pores and the phase conditions for each of the plurality of throats; 
 v. determine an updated first set of characteristics for each of the plurality of pores based on the molar balance of the components within the pore network model; 
 vi. repeat (ii) to (v) over a predetermined time at consecutive times to determine hydrocarbon extraction from the subterranean reservoir over time given the operational parameters for injection of the solvent based on changes in the molar balance of the components over time representing mass transfer of the components within the pore network model; and 
 
 d) adjust the operational parameters for injection of the solvent and repeat (c) with the adjusted operational parameters to identify operational parameters for injection of the solvent that provide a predetermined hydrocarbon extraction. 
   
     
     
         12 . The system of  claim 11 , further comprising:
 a capture device for measuring the properties of the subterranean reservoir, the properties representing the structure of the subterranean reservoir and the conditions in the subterranean reservoir, the capture device being in communication with the interface to provide the information about the properties of the subterranean reservoir;
 wherein the processor is further configured when generating the pore network model to:
 classify the properties of the subterranean reservoir representing the structure as representing pore, matrix or throat; 
 generate the pore network model using the classified properties of pore for the plurality of pores and the classified properties of throat for the plurality of throats; and 
 establish the properties representing the conditions in the subterranean reservoir as initial conditions for the pore network model, the initial conditions including liquid saturation in each of the plurality of pores. 
 
   
     
     
         13 . The system of  claim 11 , wherein the processor is further configured when defining, for each of the plurality of pores, the first set of characteristics to:
 establish a constant parameter to represent conditions used in thermodynamic flash calculations;   when the constant parameter is constant volume:
 determine the molar density of each component in the pore network model for each of the plurality of pores as the first set of characteristics; 
   when the constant parameter is constant pressure:
 determine the molar density of each component in the pore network model; and determine a mole fraction of each component based on the molar density of each component and one of a gas pressure and a liquid pressure for each of the plurality of pores as the first set of characteristics; and
 wherein the processor is further configured when deriving the second set of characteristics to: 
 determine the phase conditions in each of the plurality of pores by determining whether the components in each of the plurality of pores is in one phase or two phases where one phase is one of a liquid phase and a gas phase and two phases includes both the liquid phase and the gas phase; 
 when the constant parameter is constant volume: 
 derive, from the first set of characteristics, molar density of each component in the liquid phase, molar density of each component in the gas phase and saturation of the liquid phase for each of the plurality of pores that are in two phases as the second set of characteristics; 
 when the constant parameter is constant pressure: 
 derive, from the first set of characteristics, a mole fraction of each component in the liquid phase, a mole fraction of each component in the gas phase, saturation of the liquid phase, saturation of the gas phase for each of the plurality of pores that are in two phases as the second set of characteristics. 
 
   
     
     
         14 . The system of  claim 13 , wherein the processor is further configured when determining, for each of the plurality of throats, the phase conditions in the throat to:
 determine phase occupancy for each of the plurality of throats by determining whether the components in each of the plurality of throats is in one phase or two phases where one phase is one of a liquid phase and a gas phase and two phases includes both the liquid phase and the gas phase; and   determine phase conductivity of the liquid phase and the gas phase in each of the plurality of throats.   
     
     
         15 . The system of  claim 14 , wherein the processor is further configured when determining the molar balance of the components to:
 determine a representation for the molar balance for each component in the subterranean reservoir based on a geometry of the plurality of pores, a geometry of the plurality of throats, the first set of characteristics for each of the plurality of pores, the second set of characteristics, molar density of each component in the subterranean reservoir, the phase conductivity in each of the plurality of throats, and pressure of each phase in each of the plurality of pores;   employ a numerical analysis method to determine the molar balance for each component for each of the plurality of pores based on the representation of the molar balance for each component and the first set of characteristics for each of the plurality of pores;   determine a change in the first set of characteristics for each of the plurality of pores based on the molar balance from the numerical analysis method; and
 wherein the processor is further configured when, based on the operational parameters for injection of the solvent, performing to:
 prior to repeating (ii) to (v) over the predetermined time at consecutive times, iteratively repeat (ii) to (v) for a current time of the consecutive times until the change in the first set of characteristics is less than a predetermined change with respect to a change in the first set of characteristics from a previous iteration at the current time; and 
 
 wherein the processor is further configured when determining the updated first set of characteristics for each of the plurality of pores to:
 update the first set of characteristics for each of the plurality of pores based on the change in the first set of characteristics determined based on the molar balance from the numerical analysis method. 
 
   
     
     
         16 . The system of  claim 15 , wherein the processor is further configured when employing the numerical analysis method to determine the molar balance for each component to:
 determine a Jacobian matrix representing a rate of change of the representation of the molar balance with respect to a rate of change of the first set of characteristics; and   employing a fully implicit numerical analysis method, determine the molar balance for each component for each of the plurality of pores using the Jacobian matrix.   
     
     
         17 . The system of  claim 11 , wherein the processor is further configured when determining the updated first set of characteristics for each of the plurality of pores to:
 update the first set of characteristics for each of the plurality of pores based on the change of the molar balance of the components for a corresponding one of the plurality of pores.   
     
     
         18 . The system of  claim 11 , wherein the processor is further configured when repeating (ii) to (v) over the predetermined time to:
 before repeating (ii) to (v), adjust a time step between the consecutive times if a change in a predetermined characteristic between consecutive times is greater than predetermined amount; and   repeat (ii) to (v) at a new time which is the time step from a current time until the new time is the predetermined time.   
     
     
         19 . The system of  claim 11 , wherein the processor is further configured when repeating (ii) to (v) over the predetermined time to:
 determine the hydrocarbon extraction from the subterranean reservoir based on a difference in the molar balance in the pore network model at a previous consecutive time to the molar balance in the pore network model at a current time.   
     
     
         20 . A computer readable medium having stored thereon statements and instructions that when executed by a computer system operate the computer system to determine hydrocarbon extraction from a subterranean reservoir, the statements and instructions when executed by the computer system cause the computer system to:
 a) generate a pore network model of the subterranean reservoir representing a structure of the subterranean reservoir and conditions in the subterranean reservoir, the structure of the subterranean reservoir being represented by the pore network model as a plurality of pores connected to each other by a plurality of throats, the plurality of pores and the plurality of throats containing components including hydrocarbons;   b) establish operational parameters for injection of a solvent into the subterranean reservoir represented by the pore network model, wherein the solvent when injected becomes one of the components in at least one from the plurality of pores and the plurality of throats;   c) based on the operational parameters for injection of the solvent, perform:
 (i) define, for each of the plurality of pores, a first set of characteristics based on a molar density of each component in a pore; 
 (ii) derive, for each of the plurality of pores based on phase conditions in the pore, a second set of characteristics for the pore from the first set of characteristics for the pore; 
 (iii) determine, for each of the plurality of throats, phase conditions in a throat from the plurality of throats based on the phase conditions in ones of the plurality of pores that are connected to the throat; 
 (iv) determine a molar balance of the components within the plurality of pores and the plurality of throats in the pore network model based on the first set of characteristics and the second set of characteristics for each of the plurality of pores and the phase conditions for each of the plurality of throats; 
 (v) determine an updated first set of characteristics for each of the plurality of pores based on the molar balance of the components within the pore network model; 
 (vi) repeat (ii) to (v) over a predetermined time at consecutive times to determine hydrocarbon extraction from the subterranean reservoir over time given the operational parameters for injection of the solvent based on changes in the molar balance of the components over time representing mass transfer of the components within the pore network model; and 
   d) adjust the operational parameters for injection of the solvent and repeat (c) with the adjusted operational parameters to identify operational parameters for injection of the solvent that provide a predetermined hydrocarbon extraction.